Powers
PRUE
Prue has the ability to move objects with her mind. She first channelled her power through her eyes, and later through her hands. In Season 2, her powers grew once again and she can now astral project herself into two places at one time. In 'Morality Bites' we see that her power has grown to be very powerful and can destroy a whole room. Prue's second power came in during late season two when she found out she could astral project. This power is triggered when she feels she needs to be in two places at once.
Piper
Piper has the power to freeze time with her hands. Her power is very useful because whenever she doesn't feel like talking to someone she just freezes them and walks off. It's very useful when in a battle and she can just stop time and be a little bit a head of the enemy. In 'Morality Bites' we see her power has grown and she can stop the whole place when she is outside, not just part. But as of now, her power has grown so she can decide what she freezes and unfreezes instead of the whole room. Her second power has just come in which is speeding up and slowing down molecules. She still doesn't have total control over her new power, but has been able to blow up some nasty demons in times of need.
Phoebe
Phoebe has the power to see the past and the future, which are called premonitions. In the beginning of the season she could only see the future, but now she sees the past to. She can see it by touching an object that has a enough "psychic" energy on it. Phoebe cannot control when she has a premonition, but maybe if her powers grow enough she will be able to see the past and future whenever she likes, or even by just touching something that might have a connection. As we see in 'Morality Bites' her power will grow very strong and she can kill using her power. It was some kind of electricity. She also now is sometimes connected with demons and such so she knows there moves and thoughts and all that. Phoebe's second power came in the first episode of third season, where she found out she could levitate, she doesn't use this power much and usually levitate by accident, but occasionally just lifts her arms and is off!
Paige
Now that Prue is dead, that left the power to move things open. So as the new sister Paige has the ability to move things with her mind, but because she is half Whitelighter it works a little bit differently; instead of things physically moving to where she wants them, the object will orb over to the destination. Her second power is of course to orb, as all Whitelighters - full or half - posses the ability to orb.
Leo
Leo has the ability to heal the wounded. As found out in the episode 'Love Hurts' the power is triggered by love. He used to heal the wounded in the war and then he was given a chance to heal the wounded in magical ways and guide witches. He also has the power to orb which transports him from one place to another and which also allows him to go 'up there' to talk to 'them. Leo lost his powers for a short tie when his wings were clipped but regained them to try and save Prue.
Wyatt
Wyatt has powers we haven't yet seen in the Halliwell line, he can self heal, and when he senses danger his forcefield goes up protecting him from harm...he also has powers of a whitelighter, he can orb, and sense others.
He also has the ability to orb objects like Paige, but he can do it without having to call for things. He also has the power to blow things up just like his mother, which is odd since Piper could only stop time at first, not speed it up.
Cole
Cole being a demon had demonic powers, with all but one being lethal. His shimmering power isn't lethal and will transport hi from one place to another - much like orbing. His other power include throwing fireballs, lightning bolts, and probably many other powers. Cole has promised not to use his LETHAL powers anymore since he is now good.
WARLOCKS
All warlocks have the ability to appear in and out of places all they have to do is blink and they gone and in another place. They also have their own individual powers.
WITCHES, DEMONS, WHITE LIGHTERS, and DARK LIGHTERS
All of these creatures have their own individual powers of doing things, but also have certain powers that all of their same kind can do.